Cell cortex is a thin sheet of actin cytoskeleton spanning cell boundaries with rich out-of-equilibrium dynamics. A theoretical description of the cortex as an active fluid enables to capture cell shapes dynamics in 3D epithelial tissues. However models integrated with calibration of parameters and quantitative experiments are lacking so far. Here we report that cells in organoids and in cysts have conserved apico-basal-lateral asymmetric compositions in actin and in myosin, and we quantify their densities and mechanical properties. This allows to calibrate a new model coupling active fluids with a phase field which reproduces the main features of cell shapes. To test our approach, we successfully predict changes in cell shapes by modulating actin polymerisation in experiments and in simulations. Our study shows how active fluid theory integrated with experiments can determine cell shapes in 3D epithelial tissues.